Method for determining distances to a surface from a range image

ABSTRACT

A method determines a distance from a 3D point to a 3D surface from a 2D projected range image. A projected distance and a cliff distance from the 3D point to the 3D surface are determined using the projected range image. The projected distance and the cliff distance are then combined to determine the distance from the 3D point to the 3D surface.

FIELD OF THE INVENTION

[0001] The invention relates generally to computer graphics, and moreparticularly to range images.

BACKGROUND OF THE INVENTION

[0002] In computer graphics, it is often desired to minimize the amountof geometry in a model of a scene or an object to enable efficientrendering of the model. Several effective approaches have been developedto add visual detail to low-resolution models during rendering, such astexture mapping and bump mapping, see Apodaca et al., “AdvancedRenderman,” Morgan Kaufmann, ISBN 1558606181, 2000.

[0003] However, there are times when low-resolution models areinsufficient. For example, high-end production studios often requiremodels with detailed explicit geometry for physical simulation, e.g.,deformation and collision detection. In addition, these studios oftenemploy sophisticated illumination that requires models withhigh-resolution geometry.

[0004] Displacement mapping can be applied to the low-resolutiongeometry of an underlying model to provide correct illumination. This isan operation that is usually performed dynamically during rendering and,therefore, precludes using the resultant model with high-resolutiongeometry for physical simulation. Finally, users, such as artists,designers, engineers and sculptors, may require models withhigh-resolution geometry in order to produce solid 3D models via 3Dprinting methods.

[0005] Many Systems are known for direct modeling of the 3D geometry ofscenes and objects. However, generating models with high-resolutiongeometry is a difficult and time-consuming task. It is often very hardto recreate the complexity and variety of geometric texture that occursin nature.

[0006] High-resolution range scanners, such as Cyberware 3030, providemeans for capturing existing geometry but high-resolution scanners areexpensive and difficult to transport. In addition, their spatialresolution is limited. Hand-held range scanners are more portable, butthey too are expensive for the casual user, and sacrifice both spatialand depth resolution for portability.

[0007] In contrast, digital cameras are portable, inexpensive, have ahigh spatial resolution, and are easy to use. In addition, 2D photographediting systems such as Photoshop are dramatically simpler to use than3D modeling systems. However, digital cameras do not provide explicitdepth information.

[0008] Methods for generating the geometry for 3D models from 2D imageshave a significant connection to the field of computer vision. Manymethods are known in the prior art for extracting shape from shade,shape from focus, and shape from stereo pairs. Szeliski, in “DeterminingGeometry from Images”, SIGGRAPH 1999 Course Notes #39, Image-BasedModeling, Rendering, and Lighting, 1999, presents a bibliography and anoverview of the various approaches.

[0009] Prior work has primarily focused on developing automatictechniques for acquiring an accurate global shape description of objectsor scenes. In contrast, it is desired here to capture the spirit of thegeometry in a scene using interactive methods by capturing finegeometric detail from a 2D image. Then, a user actively involved in theprocess can modify and enhance a global shape description of objects orscenes. Thus, the goal of the present invention is quite different fromthe goal of methods in computer vision.

[0010] Although texture synthesis methods, such as described by Efros etal., “Image Quilting for Texture Synthesis and Transfer,” SIGGRAPHProceedings, pp. 341-346, 2001, can be extended to generate syntheticrange images, those techniques lack “directability.” Directability is aphrase often used in the animation industry for processes that provideprecise control over every detail.

[0011] The basic prior art approach known for constructing 3D modelsfrom range data is shown in FIG. 1. A range scanner 110 acquires rangedata 102 of a scene or object 101. Hereinafter, the term “scene” 101means a natural outdoor scene, an indoor scene, or a scene that containsone or more objects, or combinations thereof. Of particular interest arehighly textured scenes, for example, a rocky surface, leaves, grass, andthe like, and objects with uneven and complex surface structures. Therange data 102 can be processed 120 to form range images 103 and range3D surfaces 104. A method for reconstructing the geometry 130 is used togenerate a 3D model 105 from the range images 103 and range surfaces104.

[0012] There are many reconstruction methods in the prior art. A reviewof these methods is described by Curless, “From range scans to 3Dmodels”, Computer Graphics, Volume 33, No. 4, 1999. Some methods firstdetermine an implicit representation of the surface, usually in the formof a sampled distance field, and then reconstruct the 3D model as a 3Diso-surface of the implicit representation. Some methods are designed tobe very general, e.g., they can accept range data in the form of anunorganized cloud of surface points. Other methods use range data thatare available in the form of range images, where range measurements areacquired in a regularly sampled 2D grid.

[0013] There are several methods for reconstructing 3D models from rangedata that make use of distance fields. Some of these methods make thegeneral assumption that data are available only as an unorganized set ofsurface points. Hoppe et al., in “Surface Reconstruction fromUnorganized Points,” Proceedings SIGGRAPH'92, pp. 71-78, 1992, generatesa regularly sampled signed distance volume by defining local tangentialplanes from neighborhoods of scanned surface points and computing signeddistances to these planes. Marching Cubes, described by Lorensen et al.,in “Marching Cubes: a High Resolution 3D Surface ReconstructionAlgorithm,” Proceedings SIOGRAPH'87, pp. 163-169, 1987, is then used togenerate a surface model from the volume representation.

[0014] Bajaj et al. in “Automatic Reconstruction of Surfaces and ScalarFields from 3D Scans,” Proceedings SIGGRAPH'95, pp. 109-118, 1995, andBoissonnat et al., in “Smooth Surface Reconstruction via NaturalNeighbor Interpolation of Distance Functions,” in Proceedings of the16th Annual ACM Symposium on Computational Geometry, pp. 223-232, 2000,build Voronoi diagrams from scanned surface points. Then, they use theVoronoi diagram to efficiently evaluate closest distances to the surfaceand to define surface patches for the model.

[0015] Carr et al., in “Reconstruction and Representation of 3D Objectswith Radial Basis Functions”, Proceedings SIGGRAPH2001, pp. 67-76, 2001,fit a radial basis function to a set of on-surface and off-surfacepoints derived from scanned surface points. The on-surface points areassigned a value of zero, while off-surface points constructed from theon-surface points are assigned a value equal to their assigned distancefrom the surface.

[0016] All of these methods are quite general because they can beapplied to a set of unorganized points. However, when range data areavailable in the form of range images, it is desired to determine adistance field directly from the range images.

[0017] Curless et al., in “A Volumetric Method for Building ComplexModels from Range Images,” Proceedings SIGGRAPH'96, pp. 303-312, 1996,Hilton et al., in “Reliable Surface Reconstruction from Multiple RangeImages,” Proceedings of the 4th Eurographics Conference on ComputerVision, pp. 117-126, 1996, and Wheeler et al., in “Consensus surfacesfor Modeling 3D Objects from Multiple Range Images,” Proceedings of theInternational Conference of Computer Vision, 1998, present methods thatgenerate a volumetric representation of the distance field from rangesurfaces, which are generated by connecting nearest neighbors in therange image with triangular facets.

[0018] Those methods avoid triangulation over possible occlusions in themodel surface by not connecting neighbors with significant differencesin range values. That approach is conservative and avoids buildingsurfaces over unobserved regions. However, that method can lead to holesin the model that must be addressed separately as described by Curlesset al. Those three methods all use a weighted averaging scheme tocombine distance values from multiple scans. As for the method of Hoppeet al., those methods use Marching Cubes to generate a triangle modelfrom the volume representation.

[0019] Curless et al. use line-of-sight distances and only computedistances in a limited shell surrounding the surface. The distancevolume is run-length-encoded to reduce storage and processing times.Hilton et al. determine Euclidean distances from range surfaces in alimited shell surrounding the surface, and store the results in aregularly sampled volume. Wheeler et al. also determine Euclideandistances from range surfaces, but limit distance evaluations to thevertices of a three-color octree.

[0020] Whitaker, in “A Level-Set Approach to 3D Reconstruction fromRange Data,” the International Journal of Computer Vision, pp. 203-231,1998, determines line-of-sight distances directly from range images andcombines distance values from multiple scans using a windowed, weightedaverage. Then, he uses level set methods to reduce scanner noise byevolving a surface subject to forces that attract the surface to thezero-valued iso-surface of the distance field, and satisfy a shape priorsuch as surface smoothness. Zhao et al., in “Fast Surface Reconstructionusing the Level Set Method,” Proceedings 1st IEEE Workshop onVariational and Level Set Methods, pp. 194-202, 1998, use a methodsimilar to Whitaker, but initialize the distance field used to attractthe evolving surface from a set of unorganized points.

[0021] Recently Perry et al. in “Kizamu: A System for Sculpting DigitalCharacters,” Proceedings SIGGRAPH 2001, pp. 47-56, 2001 and Sagawa etal., in “Robust and Adaptive Integration of Multiple Range Images withPhotometric Attributes,” Proceedings IEEE Computer Society Conference onComputer Vision and Pattern Recognition, volume 2, pp. 172-179, 2001,describe methods similar to the method of Wheeler et al., but useadaptively sampled distance fields (ADFs) instead of a three-coloroctree to reduce the number of distance evaluations required.

[0022] ADFs adaptively sample a distance field of a scene or object andstore the sample values in a spatial hierarchy, e.g., an octree, forfast processing, see Frisken et al. “Adaptively sampled distance fields:a general representation of shape for computer graphics,” ProceedingsSIGGRAPH 2000, pp.249-254, 2000. ADFs are memory efficient and detaildirected, thus permitting very complex objects to be manipulated ondesktop machines. In addition, ADFs are a volumetric representation thatcan be used to build upon volumetric approaches for reconstructinggeometry from range data.

[0023] ADFs are described in detail in U.S. patent application Ser. No.09/370,091, “Detail directed hierarchical distance fields,” filed byFrisken at al. on Aug. 6, 1999, incorporated herein by reference. ADFmodels generated using the present invention can be incorporated into anexisting ADF sculpting system that provides an intuitive interface formanually editing the generated ADF, see U.S. patent application Ser. No.09/810,261, “System and method for sculpting digital models,” filed byPerry et al., on Mar. 16, 2001, incorporated herein by reference, andfor creating level-of-detail (LOD) triangle models from the ADF, seeU.S. patent application Ser. No. 09/810,830, “Conversion of adaptivelysampled distance fields to triangles,” filed by Frisken et al., on Mar.16, 2001, incorporated herein by reference.

[0024] There also exist several methods for generating 3D models fromheight fields or elevation maps that are related to the reconstructionof geometry from a single range image, H. Hoppe, “Smooth View-DependentLevel-of-Detail Control and its Application to Terrain Rendering,” IEEEVisualization, pp. 35-42, October, 1998. Those methods are focused onproviding efficient rendering and effective visualization, but nottowards subsequent editing, as desired here.

[0025] Therefore, it is desired to combine the advantages of inexpensivedigital cameras and 2D editing systems to provide a simple, fast, andcost-effective method for generating the geometry and detailed texturefor 3D models directly from 2D images.

SUMMARY OF THE INVENTION

[0026] It is an object of the invention to provide a method foracquiring textured range images from 2D photographs.

[0027] It is also an object of the invention provide a method forcomputing distances from range images in order to convert the texturedrange images interactively to 3D models.

[0028] It is also an object of the invention to provide an interactivemethod for acquiring detailed geometry and texture for 3D models using adigital camera and a 2D image editor.

[0029] Although these methods can be worked alone, e.g., the texturedrange image produced by the interaction method can be converted to 3Dmodels by reconstruction methods that use other means to computedistances, the combination of the methods provides a means forgenerating detailed 3D models that is cost-effective, (e.g., by usinginexpensive digital cameras and significantly reducing labor),practical, (e.g., cameras can go many places range scanners cannot),approachable, (e.g., cameras and 2D editors are simple to use, whilerange scanners and 3D modelers are not), robust (e.g., hole-free,water-tight models are produced), and efficient (e.g., model generationtakes seconds on a desktop machine).

[0030] Therefore, the invention provides a method to construct thegeometry and surface texture of 3D models from range images. Morespecifically, the range image can be highly textured. The method can beapplied to a single image or multiple images. The method is fast andmemory efficient, and provides water-tight, hole-free models, which canbe trivially sculpted in 3D to repair occluded regions.

[0031] The invention also provides an interactive method for generating3D models from images acquired by an inexpensive digital camera. Themethod generates textured range images from photographs. The texturedrange images can be used, with a construction process, as a simple andeffective way to generate the geometry and texture of models withexquisite detail.

[0032] These two methods can be combined with a 3D digital sculptingsystem to provide a powerful new design approach for generating andediting detailed 3D models.

[0033] More particularly, a distance from a 3D point to a 3D surfacefrom a 2D projected range image is determined. A projected distance anda cliff distance from the 3D point to the 3D surface are determinedusing the projected range image. The projected distance and the cliffdistance are then combined to determine the distance from the 3D pointto the 3D surface.

BRIEF DESCRIPTION OF THE DRAWINGS

[0034]FIG. 1 is a flow diagram of a prior art method for converting 2Drange data to 3D models;

[0035]FIG. 2a is a diagram of projected and Euclidean distances;

[0036]FIG. 2b is a diagram of a discontinuous surface with a cliff;

[0037]FIG. 3 is a flow diagram of a method for determining a distance toa surface from a range image using a projected range distance and adistance to a cliff according to the invention;

[0038]FIG. 4 is a flow diagram of a method for generating a cliffmapfrom a projected range image according to the invention;

[0039]FIG. 5 is a flow diagram of a method for determining a distance toa surface from a range image using a corrected projected range distance,a distance to a cliff, and a gradient magnitude image according to theinvention;

[0040]FIG. 6 is a flow diagram of a method for generating an adaptivelysampled distance field of a scene from a range image according to theinvention;

[0041]FIG. 7 is a flow diagram for generating a textured range imageaccording to the invention; and

[0042]FIG. 8 is a schematic of a camera for acquiring textured rangeimages according to the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0043] Projected Distances

[0044] Two-dimensional (2D) range images provide a 2D grid ofline-of-sight distances from a scanner to an object. A line-of-sightdistance is measured along a viewing ray from the scanner to the object.In the following description, we assume that each distance value in therange image represents a perpendicular projected distance, where thedistance is measured along a ray from the scanner to the object that isperpendicular to the plane of the scanner, also see U.S. Pat. No.6,262,738 issued to Gibson, et al. on Jul. 17, 2001, “Method forestimating volumetric distance maps from 2D depth images,” incorporatedherein by reference, for further details on this problem.

[0045] Scanning systems do not always provide projected distances butconversion to this form can be straightforward. As an example, laserstriping systems “fan” a laser beam into a plane of laser light so thateach scan line of the range image samples line-of-sight distances alongrays radiating from the point laser source to the object. Given thegeometry of the laser striping system and an angle of each ray to thelaser source, these line-of-sight distances can be converted toprojected distances and mapped back onto the plane of the scanner.Resampling these mapped projected distances into a regular grid providesthe required projected range image. This conversion can result in someloss of data near occluded regions, however, the loss is usually small.

[0046] Euclidean Distances

[0047] Curless et al. use line-of-sight distances, while Whitaker usesprojected distances in their distance-based reconstruction methods, seeabove for citation. Our method determines Euclidean distances becauseEuclidean distances provide a more accurate representation of both thedirection to the surface for points that are not on the surface, and ofthe surface itself when combining multiple scans. Euclidean distancespermit faster generation of an adaptively sampled distance field (ADF),and provide better compression of the distance field in the ADF, thusenabling the representation of high resolution models.

[0048] The projected distance can vary significantly from the Euclideandistance in two ways as shown in FIG. 2. First, when a surface 201 is atan angle 204 to a scanning direction 202, the true distance value 203 issmaller than the projected distance value 202. Second, the range imagedoes not represent distances to occluded surfaces and surfaces that arenearly parallel with the scanning direction.

[0049] At such surfaces, projected distances in the range image arediscontinuous and result in an interface in the projected distance fieldwhere large positive and large negative distances can be located inadjacent samples. While the projected distance field has the samezero-value iso-surface as the Euclidean distance field, the gradient ofthe projected distance field differs from the gradient of the trueEuclidean distance field. This can be problematic for methods that usethe distance field gradient to evolve a surface towards the zero-valueiso-surface.

[0050] In addition, when multiple range images are combined, projecteddistances from different view directions are scaled differently. If thedistances from all scans are linearly averaged, then the resultantzero-valued iso-surface of the combined projected distances stillrepresent the object surface accurately. However, most methods use awindowed, weighted, non-linear averaging of distance values fromdifferent scans. This results in artifacts in the surface where twoscans overlap.

[0051] In addition to accuracy, there are practical reasons forpreferring Euclidean distances when using ADFs. First, when one isprimarily interested in the distance field near the surface, cellsubdivision can be terminated early during ADF generation when a cell isguaranteed not to contain the surface. With Euclidean distances, wheredistance values are proportional to cell size, it is easy to determineif a cell does not contain the surface from the cell's distance values.For example, if every cell distance value has the same sign AND theabsolute magnitude of every cell distance value is greater than one halfthe cell diagonal, then the cell is either interior or exterior, anddoes not intersect the surface.

[0052] However, projected distances are not proportional to cell size.Instead, projected distances are scaled depending on the angle of thesurface to the scanning direction and are discontinuous near occludedsurfaces. Hence, using projected distances precludes the use ofterminating cell subdivision early and typically requires more than anorder of magnitude more distance evaluations and significant temporarystorage during ADF generation. Another reason for preferring Euclideandistances is that with a projected distance field, discontinuities inthe projected distance field near occluded surfaces force cells nearthese occluded surfaces to be subdivided to the highest level of theADF. This results in increased memory requirements similar to that of athree-color octree.

[0053] Correcting Projected Distances

[0054] As shown in FIG. 2a, for points near a planar surface 201, theEuclidean distance 203, d_(t), is equal to the projected distance 202,d_(p), multiplied by cos(θ) where θ 204 is the angle between thescanning direction and the surface normal, i.e., d_(t)=d_(p)* cos(θ).Given a plane with equation Ax+By+Cz+D=0 and normal (A, B, C) 203, theprojected distance, d_(p), from a point p=(p.x, p.y, p.z) to the planealong the z direction is

d _(p) =p.z−(−p.x*A/C−p.y*B/C−D/C).

[0055] Differentiating, the gradient of the projected distance field,∇(d_(p)), is

∇(d _(p))=(A/C, B/C, 1), with magnitude,

|∇(d _(p))|=(A ² +B ² +C ²)^(1/2) /C.

[0056] Thus, |∇(d_(p))|=1/cos(θ) because the normal to the plane is (A,B, C). Hence, for planar surfaces, d_(t)=d_(p)*cos(θ)=d_(p)/|∇(d_(p))|,i.e., we can correct the projected distance field near relatively planarregions of the surface by dividing the projected distance by a magnitudeof a local gradient of the projected distance field. This correctionresults in a better approximation of the Euclidean distance near smoothsurfaces.

[0057] Making this correction for a regularly sampled volume isstraightforward but slow. We sample the projected distance field foreach point in the 3D volume to generate a projected distance volume andthen correct the projected distance at each sample point by dividing bythe local gradient magnitude computed using, for example, centraldifferences.

[0058] A method for generating a volumetric distance map from projectedrange images that corrects projected distances with the gradientmagnitude is described in U.S. patent application Ser. No. 09/809,682“System and method for correcting range data to 3D models,” filed byFrisken et al., on Mar. 16, 2001, incorporated herein by reference.However, that method first generates a distance volume of the object anddetermines the magnitude of the 3D gradient from the distance volume.

[0059] In contrast, our method does not require a distance volume.Instead, the gradient magnitude is determined directly from the 2D rangeimage, or from a 2D gradient magnitude correction image that isdetermined directly from the 2D range image. In the directionperpendicular to the range image, the projected distance to the objectdecreases at a constant rate. Hence, the gradient of the projecteddistance field is constant along rays perpendicular to the range image.This means that the gradient of the 3D projected distance field can befully represented by a 2D field in the plane of the range image. This 2Dfield and the associated gradient magnitude of the 3D projected distancefield can be determined for each image point and stored in a 2D gradientmagnitude correction image as follows.

[0060] Allocate storage for a gradient magnitude correction image of thesame dimensions as the range image. Then, for each pixel in the rangeimage, determine a local 2D gradient, (dx, dy), of the range image usinga method such as central differences, determine the gradient of the 3Dprojected distance for this pixel as (kx*dx, ky*dy, 1), where kx and kyare scales related to the size of the image, e.g., kx is the width ofrange image and ky is the height of range image, determine the inversegradient magnitude as one divided by the magnitude of the gradient ofthe 3D projected distance, and store the inverse gradient magnitude inthe gradient magnitude correction image.

[0061] Hence, the projected distance value can be derived directly froma range image and corrected using a value interpolated from the gradientmagnitude correction image.

[0062] Correcting Distances Near Cliffs

[0063] Range values are discontinuous between pixels in the range imagenear occluded surfaces and surfaces that run nearly parallel to thescanning direction. Prior art methods that use range surfaces handlethese discontinuities by not triangulating over these pixels. However,this results in holes in the range surface and possibly in the resultant3D model that must be specially treated, or addressed separately.

[0064] Here, as shown in FIG. 2b, instead of discarding data near thesediscontinuities, we make the assumption that a surface 211 is continuousacross a range image discontinuity, and forms a cliff 212 that runsnearly perpendicular to the range image and connects pixels on each sideof the discontinuity. This approach eliminates holes in thereconstructed surface and provides a reasonable guess at regions of thesurface for which there is no data available. Note that this method doesnot necessarily provide accurate distances to occluded surfaces.However, we assign a low priority to distances computed for cliffs whencombining multiple scans so that distances from range images with betterviews of an occluded region are favored over cliff distances.

[0065] As shown in FIG. 3, a distance 306 to a 3D surface at a 3D querypoint p 301 is determined as follows. Determine the projected distance303 by interpolating 310 a 2D projected range image 302. The projectedrange image can be acquired by a line-of-sight range scanner, e.g., acamera or the z-buffer of a graphics processor. Determine a cliffdistance 305. As described below, the cliff distance can be determinedby interpolating 320 a cliffmap 304. Finally, combine 330 the projecteddistance 303 and the cliff distance 305 to determine the distance 306.The combining method 330 can select the smaller of the projecteddistance 303 and the cliff distance 305.

[0066] Cliff pixels, which are pixels that are beside a discontinuity inthe range image, can be detected and marked in the range image during apre-processing step. However, computing cliff distances from these cliffpixels using existing methods is still a time consuming operation.Recall that we propose using cliff distances to remove discontinuitiesin the 3D distance field in order to reduce generation times. Even ifcliff pixels are binned in a spatial hierarchy and a fast searchtechnique is used to locate nearest cliff pixels, this approach doesstill not provide a significant improvement over simply requiringcomplete three-color octree subdivision of the ADF along the cliffs.

[0067] Fortunately, 3D cliff distances can be estimated from anannotated 2D image, or the cliffmap 304, that can be computed prior togeneration. From FIG. 2b, the cliffmap encodes distances to the top 221and bottom 222 of the nearest cliff 212 in the surface 211 for eachpixel in the range image as well as the heights, i.e., the projectedrange values, of the top and bottom of the cliff 212.

[0068]FIG. 4 shows a method 440 for determining the cliffmap 304 for aprojected range image 302. First, allocate storage for two distancevalues and two cliff heights for each pixel in the projected range image302. Initialize 410 cliff pixels to determine an initialized cliffmap401. The initial cliff distances for each pixel are set to the largestpossible positive value. Then, for each pixel in the range image,determine if the pixel is a top and/or bottom cliff pixel by looking atthe pixel's range value relative to range values of adjacent pixels. Ifthe difference between adjacent range values is greater than apredetermine threshold, a discontinuity in the surface can be assumed.If the pixel is a cliff top or a cliff bottom pixel, set thecorresponding (top or bottom) cliff distance(s) to zero and thecorresponding cliff height(s) to be the pixel's range value.

[0069] Contiguous 1-pixel wide cliffs can be reduced 420 to a singlemulti-pixel wide cliff 402 by setting pixels tagged as both top andbottom cliffs to non-cliff pixels, e.g., by setting both their cliffdistances to large positive value.

[0070] Finally, determine 430 the cliff distances and cliff heights forall non-cliff pixels in the cliffmap 304. This can be done by firstsetting unsigned distances to closest cliff pixels together with thecorresponding cliff heights using a distance transform, e.g., a 3×3neighborhood Euclidean transform, and second negating cliff distancesfor pixels that are on the outward side of a cliff.

[0071] To determine the cliff distance 305 from the query point 301, tothe nearest cliff using the cliffmap 304, first obtain, e.g., byinterpolating the cliffmap 304, the distances to the closest cliff topand cliff bottom and the corresponding heights of the cliff top andcliff bottom. Next, determine whether the query point 301 is closest tothe top of the cliff, the bottom of the cliff, or the face of the cliffby comparing the range value of the query point 301 to the heights ofthe cliff top and bottom. If the query point is above the cliff top,then the cliff distance is determined as the distance to the top of thecliff. If the query point is below the cliff bottom, then the distanceis determined as the distance to the bottom of the cliff. Otherwise, thequery point 301 is closest to the face of the cliff, and the distance isdetermined as the distance to a line connecting the cliff top to thecliff bottom.

[0072] Estimating the Euclidean Distance

[0073]FIG. 5 shows the steps 540 to determine the Euclidean distance 306at the query point 301 for a single range image. The projected distance303 is interpolated 310 from the projected range image 302. Theassociated gradient magnitude 502 is interpolated 510 from the gradientmagnitude correction image 501. The projected distance is corrected 520with the gradient magnitude 502 to determine the corrected projecteddistance 503. The distance 305 to the nearest cliff is determined 320using the cliffmap 304. Finally, the smaller of the corrected projecteddistance and the cliff distance is selected 530 to determine thedistance 306.

[0074] Combining Multiple Range Images

[0075] Distances from multiple scans can be combined in several waysdepending on the method used for reconstructing surfaces. For example,one could use any of the weighted averaging schemes described by Curlesset al., Hilton et al., Wheeler et al., and Whitaker, see above forcitation. The best combining method is determined by the noisecharacteristics of the range scanner and any further processing appliedby the reconstruction method.

[0076] For example, a simple combining scheme selects a ‘best’ distancevalue from multiple scans, where ‘best’ means that small distances arefavored over large distances, distances with small gradient magnitudesare favored over distances with large gradient magnitudes, and correctedprojected distances are favored over cliff distances.

[0077] Generating an Adaptively Sampled Distance Field

[0078]FIG. 6 shows the steps for generating an ADF of the Euclideandistance field. First, range images 601 are acquired 610, and converted620 to projected range images 602. These projected range images arepre-processed to determine 630 the gradient magnitude correction image501 and to determine 440 the cliffmap 304.

[0079] Starting from the root cell of the ADF, the ADF generator 640recursively subdivides the cells of the ADF 606 using an error-basedsubdivision predicate until the field within the cell is well describedby the cell's 8 distance values. Distances at each ADF query point 603are evaluated 540 for each range image to produce distances for eachrange image 604 that are combined 650 to determine the distance 605 atpoint p. For this application, surface-centric ADFs that limitsubdivision to cells bounding the surface and do not subdivide exterioror interior cells beyond a minimum level in the ADF hierarchy are used.

[0080] We also use the method as described above to generate thegeometry from a textured range image produced by an interactive methoddescribed below.

[0081] Generating Textured Range Images from Photographs

[0082] Extracting Detailed Geometric Texture from Photographs

[0083] As shown in FIG. 7, we also provide an interactive method forgenerating range images from a pair of photographs, that is, two 2Dimages without explicit depth information. However, instead of using apair of stereo images that are offset from each other, as is typicallydone in the prior art, our images, surprisingly, are substantiallyaligned on the same optical axis. That is, the two photographs are takenfrom substantially the identical point of view.

[0084] A first image 701 is taken of the scene 101 with a camera 800under ambient lighting. The camera 800 is described in greater detailbelow. With the camera 800 at the same location, a second image 702 istaken with directed lighting, for example, a flash substantiallyco-located with the lens of the camera 800.

[0085] An intensity compensated image is derived 710 from the pair ofphotographs 701-702. We call this image a textured range image 703. Auser can optionally edit and enhance 720 the textured range image 702using a 2D image editor 721. A 3D model 704 is then generated 730 fromthis enhanced textured range image 703 using the method described above.The last two steps can be repeated until the desired result is achieved.

[0086] Compensating for Intensity Variation Using Directed Lighting

[0087] Photographs contain a great deal of information about thegeometry and texture of an object or scene. For example, in a photographof a stone wall, cracks between the stones are darkened by shadows,while protruding parts of the stones appear brighter. This is a commonphenomenon when the first image 701 that is acquired of the scene 101 isilluminated by ambient light. Highlights tend to brighten raisedportions of a surface, and shadows tend to darken recessed portions ofthe surface. Light and dark intensity variation in the surface oftendominate this effect.

[0088] However, in a photograph taken with direct light, the recessedand raised portions of the photograph tend to be illuminated much moreevenly. Because the lens and flash are substantially co-located, thereare almost no shadows present in the image 702 acquired under directlighting conditions. In contrast with prior art stereoscopic pairs ofimages, the second image is essentially acquired from the identicalpoint of view.

[0089] The second photograph 702 records light intensity variation ofthe scene without the depth cues provided by shadows in the naturallyilluminated first photograph 701. This suggests using the flash image702 to compensate 710 for intensity variation in the ambient lightedphotograph 701.

[0090] Therefore, we compensate 710 for intensity variation by dividingthe luminance of each pixel of the ambient lighted image 701 by theluminance of the corresponding pixel in the directly lighted image 702to obtain the intensity compensated image 703. We perform intensitycompensation using floating point arithmetic to avoid discretizationartifacts. In the intensity compensated image, the intensity variationhas been eliminated, but the depth cues remain. In fact, we use theintensity compensated image as an approximate textured range image togenerate 740 the 3D geometry of model 704 of the scene 101.

[0091] Experimenting with different cameras and different lighting, wemake the following observations. First, we find that “ambient lighting”encompasses a broad range of lighting conditions including outdoor andindoor lighting, sunny and overcast conditions, and images taken in ashadow or in sunlight. All that is required is that shadows in the sceneemphasize the desired detailed geometry and that the direct lightdominates background lighting, particularly during short exposures.

[0092] Any number of exposure and film settings could be used, however,we find that photographs taken using the defaults automatic exposuresettings of the camera 800 typically achieve the best results. The bestresults are achieved when the highest possible resolution image is used,i.e., image compression is disabled.

[0093] If the camera 800 is mounted on a tripod 711, then there can be adelay between acquiring the ambient and flash images, and the two imagesare still substantially aligned. Alternatively, the camera can beconfigured to take the ambient and flash image in rapid succession, sothat camera motion is negligible, even when the camera is hand-held. Itis also possible to take a sequence of pairs of images using a videocamera, and generate a sequence of intensity compensated images. Thiscan provide an interesting new source for producing animations. Forexample, if the video camera takes 60 frames per second, then this willproduce 3D textured range images or 3D video. This is adequate for mostanimation.

[0094] We compared two digital cameras, a Nikon Coolpix 775, which is areasonable quality consumer camera with 8-bits per channel resolution,and a Canon D30, which is a high-end professional camera with 12-bitsper channel resolution. We are able to achieve very good results withboth cameras and find that the textured range images obtained with thelower resolution camera suffice for most applications.

[0095] Enhancing Textured Range Images Using a 2D Editor

[0096] In an interactive method, the textured range image or 3D model703 is enhanced with the 2D image editor 721, such as Adobe Photoshop,to clean up and enhance features. For example, white pixels that occurwhere there were shadows in the flash image 702 can be removed.

[0097] The textured range image 703 can also be enhanced by the 2D imageeditor 721 by combining it with directed gradient filters to enhance theshape or curvature of selected features in the textured range image,with images such as elevation maps, height fields, or range images toprovide global shape for the 3D model 704, and by other images such asprocedurally generated images to add synthetic texture to the 3D model.

[0098] In addition, the textured range image 703 can be enhanced in the2D image editor using 2D image brushes that locally affect the rangevalues. For example, gradient-based brushes can be used to raise orlower local regions of the 3D model, brushes with a procedural-basedtexture can be used to add local texture detail, and brushes derivedfrom range images such as textured range images or elevation maps couldbe used to add local features. For example, a brush with pixel valuesrepresenting the elevation data for a mountain could be used to add amountain range to the 3D model by swiping the mountain brush over thetextured range image.

[0099] Enhancing the textured range image 702 is fast and easy becauseof the sophisticated tools available for image editing. This editingprocess produces the enhanced textured range image, which can beconverted 730 to the 3D model 704 using the above described method. Theconversion only takes a few seconds, thereby providing an effectivefeedback loop for design.

[0100] Final 3D Editing

[0101] When satisfied with the results of the interactive editingdescribed above, we can then sculpt 740 the model 704 in 3D using theADF sculpting system to edit features, that are impossible to edit in2D, e.g., deep recesses and large overhangs.

[0102] 3D Camera for Acquiring Textured Range Images

[0103]FIG. 8 shows the camera 800 in greater detail. The camera 800 hasa single lens 801, and a flash 802 substantially co-located with thelens 801. A first image 811 is acquired with ambient light 803, and asecond image 812 with the flash 802 producing directed light 804. Theorder of acquiring the images is not important. The images 811-812 arestored in a memory 830. A processor 820 performs the intensitycompensation as described above to generate the textured range image813. The intensity compensation is performed by dividing the luminanceof each pixel of the ambient lighted image 811 by the luminance of thecorresponding pixel in the directly lighted image 812 to obtain theintensity compensated image 813. The textured range image 813 can thanbe exported to other systems via an interface 840, e.g., a USB port. Itshould be noted that the camera can take a sequence of images to producea 3D video 850.

[0104] Effect of the Invention

[0105] We have described interactive methods for acquiring 3D geometryand texture using an inexpensive digital camera. The method generatestextured 3D range images from 2D photographs that can be used togenerate geometry and texture with exquisite detail. We have alsodescribed a method for reconstructing 3D geometry from range images. Thecombination of these two techniques provides a means for generatingdetailed 3D models that is cost-effective, practical, approachable,robust, and efficient.

We claim:
 1. A method for determining a distance from a 3D point to a 3Dsurface from a 2D projected range image comprising: determining aprojected distance from the 3D point to the 3D surface using theprojected range image; determining a cliff distance from the 3D point toa nearest cliff in the 3D surface using the projected range image; andcombining the projected distance and the cliff distance to determine thedistance from the 3D point to the 3D surface.
 2. The method of claim 1further comprising: interpolating the projected range image at the 3Dpoint to determine the projected distance.
 3. The method of claim 1wherein the combining further comprises: selecting the smaller of theprojected distance and the cliff distance as the distance from the 3Dpoint to the 3D surface.
 4. The method of claim 1 further comprising:interpolating a cliffmap at the 3D point to determine the cliffdistance.
 5. The method of claim 4 further comprising: allocatingstorage to represent a top and bottom cliff distance and a top andbottom cliff height for each pixel in the projected range image;determining, for each pixel in the projected range image, if the pixelis a top or bottom cliff pixel; setting, for each cliff pixel in thecliffmap, the top cliff distance to zero and the top height to acorresponding range value if the pixel is a top cliff pixel, and settingthe bottom cliff distance to zero and the bottom cliff height to thecorresponding range value if the pixel is a bottom cliff pixel; anddetermining the cliff distance and cliff height for all other pixels inthe cliffmap.
 6. The method of claim 5 wherein the cliff distances areassigned.
 7. The method of claim 1 further comprising: correcting theprojected distance by a corresponding gradient magnitude of a gradientmagnitude correction image.
 8. The method of claim 7 wherein thegradient magnitude correction image comprises a 2D image having eachimage value determined from a gradient of the 2D projected range image.9. The method of claim 1 wherein the 2D projected range image isdetermined from a line-of-sight range image acquired by a range scanner.10. The method of claim 1 wherein the 2D the projected range image isdetermined from a z-buffer of a graphics processor.
 11. The method ofclaim 1 wherein the 2D projected range image is textured.
 12. The methodof claim 1 wherein the 2D projected range image is a height field. 13.The method of claim 1 wherein the 2D projected range image is anelevation map.
 14. The method of claim 1 wherein the 2D projected rangeimage is an arbitrary 2D image.
 15. The method of claim 1 wherein aplurality of distances at the 3D point are determined from a pluralityof 2D projected range images, and further comprising: combining theplurality of distances into a combined distance from the 3D point to the3D surface.
 16. The method of claim 1 wherein a plurality of distancesat a plurality of 3D points are determined to sample a distance field ofthe 3D surface.
 17. The method of claim 16 wherein the distancerepresents a 3D model.
 18. The method of claim 16 further comprising:storing the distance field as a regularly sampled volume data set. 19.The method of claim 18 further comprising: generating a surface model ofthe 3D surface from the regularly sampled volume data set.
 20. Themethod of claim 16 further comprising: storing the distance field as anadaptively sampled distance field.
 21. The method of claim 20 furthercomprising: generating a surface model from the adaptively sampleddistance field.